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Title: Optimal control of systems with intermediate phase constraints

Abstract

In this paper, we derive necessary conditions of minimum for the general optimal control problem with the following characteristics: the trajectory is corrected at intermediate time instants using matching relationships; the system dynamics may vary in each time interval; the optimand functional and the functional constraints depend on the intermediate time instants, the momenta, and the phase coordinates of the trajectories. The result is derived by the methods of modern optimization theory and nonsmooth analysis. It is presented in the form of a maximum principle. The specific solution scheme for this problem has been developed in greater detail elsewhere for systems of the form x{sub i}={line_integral}{sub i}(t, x{sub i}). Much of the previous manipulations and results on the structure of the conjugate cone and the form of the directional derivatives are used also in this paper. This is legitimate because the optimized parameters and controls are independent.

Authors:
Publication Date:
OSTI Identifier:
457595
Resource Type:
Journal Article
Journal Name:
Cybernetics and Systems Analysis
Additional Journal Information:
Journal Volume: 30; Journal Issue: 4; Other Information: PBD: Mar 1995; TN: Translated from Kibernetika i Sistemnyi Analiz; No. 4, 104-111(Jul-Aug 1994)
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; CONTROL SYSTEMS; OPTIMIZATION; FUNCTIONALS; DIFFERENTIAL EQUATIONS

Citation Formats

Kirichenko, S B. Optimal control of systems with intermediate phase constraints. United States: N. p., 1995. Web.
Kirichenko, S B. Optimal control of systems with intermediate phase constraints. United States.
Kirichenko, S B. 1995. "Optimal control of systems with intermediate phase constraints". United States.
@article{osti_457595,
title = {Optimal control of systems with intermediate phase constraints},
author = {Kirichenko, S B},
abstractNote = {In this paper, we derive necessary conditions of minimum for the general optimal control problem with the following characteristics: the trajectory is corrected at intermediate time instants using matching relationships; the system dynamics may vary in each time interval; the optimand functional and the functional constraints depend on the intermediate time instants, the momenta, and the phase coordinates of the trajectories. The result is derived by the methods of modern optimization theory and nonsmooth analysis. It is presented in the form of a maximum principle. The specific solution scheme for this problem has been developed in greater detail elsewhere for systems of the form x{sub i}={line_integral}{sub i}(t, x{sub i}). Much of the previous manipulations and results on the structure of the conjugate cone and the form of the directional derivatives are used also in this paper. This is legitimate because the optimized parameters and controls are independent.},
doi = {},
url = {https://www.osti.gov/biblio/457595}, journal = {Cybernetics and Systems Analysis},
number = 4,
volume = 30,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 1995},
month = {Wed Mar 01 00:00:00 EST 1995}
}